A199860 Numbers k such that 6k-5 is a composite number of the form (6x-1) * (6y-1).

5, 10, 15, 20, 21, 25, 30, 32, 35, 40, 43, 45, 49, 50, 54, 55, 60, 65, 66, 70, 75, 76, 80, 83, 85, 87, 89, 90, 95, 98, 100, 105, 109, 110, 112, 115, 117, 120, 125, 130, 131, 134, 135, 140, 141, 142, 145, 150, 151, 153, 155, 158, 160, 164, 165, 168, 170, 175

Offset

1,1

Comments

Numbers whose associate in A091300 has at least one factorization into two factors of A016969.

Links

Table of n, a(n) for n=1..58.

Example

n=5 is in the sequence because 6*5-5 = 25 = 5*5 with x = y = 1.
n=10 is in the sequence because 6*10-5 = 55 = 5*11 with x=1, y=2.

Maple

isA016969 := proc(n)
    (n mod 6)=5 ;
end proc:
isA016921 := proc(n)
    (n mod 6)=1 ;
end proc:
isA091300 := proc(n)
    (not isprime(n)) and isA016921(n) ;
end proc:
isA199860 := proc(n)
    if isA091300(6*n-5) then
        for d in numtheory[divisors](6*n-5) minus {1} do
            if isA016969(d) and isA016969((6*n-5)/d) then
                return true;
            end if;
        end do:
        return false;
    else
        return false;
    end if;
end proc:
for n from 5 to 210 do
    if isA199860(n) then
        printf("%d, ", n) ;
    end if ;
end do; # R. J. Mathar, Nov 27 2011

Crossrefs

Cf. A199859.

Sequence in context: A109046 A048725 A190240 * A101889 A115772 A178891

Adjacent sequences: A199857 A199858 A199859 * A199861 A199862 A199863

Keyword

nonn,easy

Author

Eleonora Echeverri-Toro, Nov 11 2011

Status

approved